Mix flour, 2 tablespoons sugar, and salt in a food processor. Add frozen butter and pulse 4 times. Add shortening and cream cheese into flour mixture; pulse another 4 or 5 times until clumps are the size of peas.

Dump mixture into a medium bowl; rub through fingertips to blend. Stir in water with a rubber spatula until dough clumps form. Press dough with your palm to form a ball, then divide in half. Wrap each half in plastic wrap, pressing to form thick disks. Refrigerate for at least 1 hour.

Adjust oven rack to lowest position and place a pizza stone or quarry tiles on the rack to form an 18-inch square. Preheat oven to 400°F (200°C).

In a large saucepan, cook 1 cup cherry juice, sugar, potato starch, and a pinch of salt over medium-low heat. Stir until a very thick paste forms. Scrape paste into cherries in a bowl. Add almond extract and stir to combine.

Set a dough disk on a floured work surface and roll into a 14-inch circle. Fold and lift it into a 9-inch Pyrex pie plate. Fit dough into the plate without stretching. Refrigerate.

Roll remaining dough disk into a 12-inch circle. Remove pie shell from refrigerator and add fruit filling. Dot with butter. Lay the rolled dough on top, trim and flute the edges.

Set foil on the baking stone or tiles in the oven. Place the pie on the foil and bake for 20 minutes. Remove, brush with egg white and sprinkle sugar. Bake for 20 minutes more. Loosely cover the edges with foil and bake until filling bubbles, 15 to 20 minutes longer.